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The two-space extension is a very common pattern and forms a base. I've found lots of material here, and here, and elsewhere on how it cannot be cut and how to defend against various invasions.

Nevertheless, in one of my games I was confronted with the following non-standard invasion:

$$cm1 Non-standard invasion of two-space extension
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . 1 . . . . Q X . . . . |
$$ | . . . . . B . O . . O . . Q X . . . . |
$$ | . . . , . . . . . , . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

Question 1: Ignoring the three marked stones, how would one usually defend this invasion? Is J17 correct here?

Considering the option for black to connect up to the left and the white wall at the right, I played H18, which resulted in utter chaos and a miserable result for white. Below is my failed attempt at defending against this invasion.

$$cm1 Failed defense
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . 2 1 . 3 4 . Q X . . . . |
$$ | . . . . . B . O . 5 O 7 . Q X . . . . |
$$ | . . . , . . . . . 6 . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

With this, Black was able to connect to the right. I've been playing around with various options, but couldn't find anything useful.

Question 2: Is white 2 above already a horrible mistake? Or does there exist a follow-up after black 3 that kills the invading stones?

Question 3: How strong is the two-space extension? In the initial situation where black invades at 1, what is the best white can expect to get?

Question 4: I found myself at quite a lack of knowledge when it comes to defending such non-standard attacks, however, most resources (like SL) only cover the typical attacks. Is it worthwhile to invest a lot of time into learning how to deal with strange attacks? Or should one expect to get this simply by experience?

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1  
Question 4 is probably complex enough to warrant it's own post. –  goldPseudo Jan 30 '12 at 23:52
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4 Answers

up vote 11 down vote accepted

The 2 space extension is generally regarded as very hard to cut and thus solid, providing at least 1 eye with various options to gain a lot more eyespace easily.

However, invasions and attacks are still possible. The B1 move in your diagram is actually a standard invasion with the marked black stone around.

$$cm1 A possible invasion of two-space extension
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . 1 . . . . Q X . . . . |
$$ | . . . . . B . O . . O . . Q X . . . . |
$$ | . . . , . . . . . , . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

Influence

One usual aim of this move is to either create center influence like this:

$$cm1 Influence, part 1
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . 2 1 . . . . . . . . . . |
$$ | . . . . . B 9 W 3 6 W . . . . . . . . |
$$ | . . . , . . . 5 4 8 . . . . . , . . . |
$$ | . . . . . . . . 7 . . . . . . . . . . |

.

$$Wcm1 Influence, part 2
$$ +---------------------------------------+
$$ | . . . . . . . . 5 . . . . . . . . . . |
$$ | . . . . . . 4 O X 3 . . . . . . . . . |
$$ | . . . . . B X W X O W . . . . . . . . |
$$ | . . . , . . 2 X O O . . . . . , . . . |
$$ | . . . . . . . 1 X . . . . . . . . . . |

(B9 and the atari may be different on certain boards.)

$$Wcm1 Influence, result
$$ +---------------------------------------+
$$ | . . . . . . . . O . . . . . . . . . . |
$$ | . . . . . . X O . O . . . . . . . . . |
$$ | . . . . . B X W . O W . . . . . . . . |
$$ | . . . , . . X X O O . . . . . , . . . |
$$ | . . . . . . . O X . . . . . . . . . . |

This can be good depending on the global situation. Of course, white gets super strong, so black should only consider this if there is no useful attack on the 2 space extension anyway and the center is important.

Base robbing

Another idea is to use this invasion to steal eyespace and gain some territory. It is usual if there is a black stone on either side of the extension.

$$cm1 Base robbing, simple variation
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . a 1 3 b . . . . . . . . |
$$ | . . . . . B . W 2 4 W . B . . . . . . |
$$ | . . . X . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

A and B are miai to connect the stones out, so black can consider an outside move to attack - or he can firmly link up his 2 stones to either side to rid white of any sente moves near the edge.

This way, white ends up with a solid, but eyeless group with good center access. Depending on the board, this can be good for either player.

$$cm1 Base robbing, white resistance
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . 2 1 . . . . . . . . . . |
$$ | . . . . . B . W . . W . B . . . . . . |
$$ | . . . X . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

However, white may think about resisting like this. this move can be good, but usually black 1 is only played if black can follow up like this:

$$cm1 Base robbing, black counter
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . O X . 1 a . . . . . . . |
$$ | . . . . . B . W c b W . B . . . . . . |
$$ | . . . X . . . . . d . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

A and B are miai now, so the black stones are out and white has a weaker shape than by playing C to begin with. In some cases, black plays the B-D exchange before B1.

$$Bcm1 White resistance, another idea
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . 1 . . . . . . . . . . |
$$ | . . . X 2 . O . . O . X . . X . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . X . . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

Sometimes, white can try a kind-of-sente move instead of replying directly. If black answers the move, white can play more aggressively against the invasion stone. If black follows up the invasion, an exchange could take place. This should be considered carefully before invading at 1.

Depending on the board, white may dislike the invasion on the second line, and thus plays a tobi to strengthen her group:

$$Wcm1 Defend
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . e . . . . . . d . . . . . . |
$$ | . . . . . B . W . . W . B . . . . . . |
$$ | . . . X . . . . . , . . . . . X . . . |
$$ | . . . . . . . a b c 1 . . . . . . . . |

Any of A, B, C are thinkable just as well, and in some cases a tsuke at D or E is reasonable, too. This requires some reading, as D and E tend to lead to a huge exchange.

By the way, keep in mind that base robbing can be beneficial to white on certain boards. That's one of the reasons white, instead of the second line invasion, an attack at black 1 or a is usual in this shape, too, as well as moves on top of B or C.

Actual game

In the actual game, white had some extra stones to the right, which changes the situation significantly.

$$cm1 Simple answer
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . 3 1 4 . . . Q X . . . . |
$$ | . . . . . B 5 O 2 . O . . Q X . . . . |
$$ | . . . , . . . . . , . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

White could simply answer at W2, connecting firmly. Black cannot play 3 at 4 because then white would play 3 and thanks to the white stones on the right, black dies inside.

Thus black has to connect out, allowing white to get a reasonable shape with the tiger mouth at 4 in sente. Black 5 is played on the third instead of the second line because it has far greater influence on the center and the strength of the white group.

$$cm1 Strong answer
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . 2 1 . 5 . . Q X . . . . |
$$ | . . . . . B . O . 3 O 6 . Q X . . . . |
$$ | . . . , . . . . . 4 . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

White can also consider the strong-hand descend at 2, blocking the connection out. Black will play 3 and 5, to which white avoids the self-destructing reply to the right of 5 and instead simply nobis at 6. Black is now forced to find a way to connect out or live locally - I'll leave the tsumego as an exercise for the reader.

Related joseki shape

$$cm1 Simple answer
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . 2 1 . . . O . . . |
$$ | . . . . . . . . B . O . . O 3 . X . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |

In this very common joseki shape white is supposed to have a very solid group with enough eyespace to be difficult to attack. However, with the marked black stone in place, the invasion of B1 is an astonishing threat. The details are too long to list here, but if white blocks at 2, black will play the tesuji of 3 and it is very hard for white to find an answer that doesn't lose half the group, base, and yose.

Answering your further questions

Question 3: How strong is the two-space extension? In the initial situation where black invades at 1, what is the best white can expect to get?

The 2 space extension is stable. It is not alive locally, it is not strong, but it is stable in the sense of being connected and thus difficult to fiendishly attack. Prefer this extension when you don't like the idea of being split.

$$Wcm1 Solid
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . X . . . . a 1 b . O . X . . . |
$$ | . . X , . . . . . c . . . . . , X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |

For instance, in this shape, a wide extension to A would immediately be invaded at B. White could think about playing 1 at C, aiming for a light shape, but that offers a range of difficult to handle invasions that you need to be comfortable with.

Also, leep in mind that "killing" is not always the best answer to moves that are either unusual or bad. Sometimes letting the opponent live is the best punishment. Remember the idea of the sacrifice in the 'influence' section of this answer - in that case, maybe just go for center influence (connect instead of block) when the center is of more value.

And contrarily, you'll be astonished how much dan players hate living sometimes. I remember a high dan friend of mind talking about a game he played against a pro: "I lived everywhere by crawling on the second line. It was atrocious, I could not find a good way to die."

Question 4: I found myself at quite a lack of knowledge when it comes to defending such non-standard attacks, however, most resources (like SL) only cover the typical attacks. Is it worthwhile to invest a lot of time into learning how to deal with strange attacks? Or should one expect to get this simply by experience?

Midgame joseki as those presented in this answer are very useful. Either learn them by playing tons of games and remembering the best shapes, or look them up in books. I remember there was a pretty thorough discussion of the 2 space extension in "Shape up!" by Charles Matthews. Eventually, as a dan player, you'll be forced to remember them from study though since (at least Western) books rarely cover deep variations for specific boards or new inventions.

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Don't have any books available as reference right now sadly, so this is just from the top of my head - let me know if I made a mistake or if there's anything that should be further explained. –  mafutrct Jan 31 '12 at 17:49
    
I feel horrible that I can only vote once. But then, I was only browsing 2 questions for "a couple" of minutes (goodbye, morning break!) :) –  Stephen Feb 7 '12 at 19:31
    
In Related joseki shape I would play M18 L18 N17 –  Xavier Combelle Mar 24 '12 at 18:48
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Although it can and often does provide territory, that is not the primary reason that you want to play the two-space extension on the third line; what you're looking for with this extension is a base which is very difficult to cut, one which you can use to fight and/or secure territory as the game progresses. Unless black has support, white can easily connect in the face of any attack and either make life on the edge, or leap out into the centre, depending on the circumstances. It's a very stable and efficient shape, and the flexibility is a major part of why it's so popular.

Maintaining the connection itself against black 1 is fairly simple:

$$Wcm2 The easiest solution: Connect
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . X . . . . O X . . . . |
$$ | . . . . . X . O 1 . O . . O X . . . . |
$$ | . . . , . . . . . , . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

Now the so-called invasion is little more than a reduction, which now looks quite lonely. A continuation could look something like this:

$$Wcm2 Black's not-so-glorious retreat
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . 4 2 X 3 . a . Q X . . . . |
$$ | . . . . . X . O 1 . O . . Q X . . . . |
$$ | . . . , . . . . . , . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

Thanks to the marked stones white still has a very solid territory, even though black has "successfully" reduced it by a few points (in gote). Black has traded a few points of territory for giving white a not-insignificant amount of influence toward the the centre; this is the type of move that's typically held off until the endgame after territory is more-or-less defined. During the mid-game, black would usually be better off deferring the attack in favour of a big point elsewhere unless he has a good chance of profiting (e.g., by pressuring or outright killing the weakened group after reducing eyespace).

Even if the marked stones were absent, white could still comfortably jump out to the centre or secure an eye with a.

Playing white 2 at H18 isn't necessarily bad (depending on what's going on in the centre, I would probably avoid it), but it picks a fight you want to be sure that you can win, and that is actually worth winning; thinking that the best (or only) defence against any attack involves killing the offending stones is a common mistake. If black can tip the balance in his favour by ten points now, you can still win if you tip it back later by twenty, and being overly aggressive is a good way to make things needlessly complicated.

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Surely you mean that White makes life locally with M18, not N18? –  Karl Knechtel Jan 31 '12 at 8:07
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Question 1: Ignoring the three marked stones, how would one usually defend this invasion? Is J17 correct here?

They really can't be ignored for a question like this. "This" invasion doesn't come out of nowhere (except vs. a belligerent beginner).

Question 2: Is white 2 above already a horrible mistake? Or does there exist a follow-up after black 3 that kills the invading stones?

4 at 7 seems to work. Black should not have enough space to live locally.

Question 3: How strong is the two-space extension? In the initial situation where black invades at 1, what is the best white can expect to get?

I wouldn't normally expect Black to accomplish anything positive without stones in the K15 area. The P17 wall may be troublesome, though. It also needs to be asked just how White got into this position in the first place. In particular, if J18 is worrisome, then defend first.

Question 4: I found myself at quite a lack of knowledge when it comes to defending such non-standard attacks, however, most resources (like SL) only cover the typical attacks. Is it worthwhile to invest a lot of time into learning how to deal with strange attacks? Or should one expect to get this simply by experience?

By definition, you won't see strange attacks often. There's no point in memorizing responses to them, at least until you get to the point where you've memorized everything more useful than that (which is probably pretty close to pro level). What you want to do is develop your tactics and your fighting strength. Studying shape is a good idea as well (it's a broader topic than many people give it credit for).

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I played a little with 4 at 7, I don't think it actually works (though it's definitely better than 4 as is). I'll post a diagram when I get home from work. –  shujaa Jan 31 '12 at 18:21
    
I take it back, I'm not going to post it here. I started typing it up and there's more variations than I'd care to type, especially when it doesn't even answer the question. I'll side with @mafutrct's exercise left for the reader. But I don't think it's possible to completely kill the invasion. –  shujaa Feb 1 '12 at 8:56
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I would play J17 and force Black to connect.

The way you played, Black got the optimal result; he broke up your extension and turned "your" area into a free-for-all fight.

Black's downside is that his "invasion" is on the second line. If you push against him on the third line, you've lost some territory, it's true, but you've more than made up for this in center facing influence.

Many players will trade influence for third line territory, but here Black is basically offering to trade influence for only second line territory. The trade would be all in your favor.

Besides, once you hane at K18, Black has to take gote with 5 (see the diagram to gold's answer). Then you should reduce Black's right side influence, perhaps with a move around N15.

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I object: White simply building a wall on the third line here is not a great result in terms of "influence", because of the existing stones at F17 and P16. Walls that already face opposition at their endpoints - coming around the sides - are severely compromised. That said, White has probably played quite passively to get to a position like this in the first place. –  Karl Knechtel Jan 31 '12 at 8:09
    
@KarlKnechtel: I agree, white's position isn't great. But black's is worse, running on the second line, the "line of defeat." "It's all relative." –  Tom Au Feb 2 '12 at 18:46
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